The true discount on a sum of money due 2 years hence at 5% is Rs. 15. Find the sum.

Options

A. Rs. 150
B. Rs. 165
C. Rs. 170
D. Rs. 160

Answer

To solve the problem, we need to find the sum of money based on the true discount given. Let's break it down step by step.

### Step 1: Understand the given values
- True Discount (TD) = Rs. 15
- Rate (R) = 5%
- Time (T) = 2 years

### Step 2: Use the formula for Present Worth (PW)
The formula for Present Worth (PW) is given by:

\[ PW = \frac{TD \times 100}{R \times T} \]

### Step 3: Substitute the values into the formula
Substituting the known values into the formula:

\[ PW = \frac{15 \times 100}{5 \times 2} \]

### Step 4: Calculate the denominator
First, calculate the denominator:

\[ 5 \times 2 = 10 \]

### Step 5: Calculate Present Worth (PW)
Now substitute the denominator back into the equation:

\[ PW = \frac{1500}{10} = 150 \]

### Step 6: Use the formula for the Sum
The formula for the Sum (S) is:

\[ S = TD + PW \]

### Step 7: Substitute the values to find the Sum
Substituting the values we have:

\[ S = 15 + 150 = 165 \]

### Final Answer
The sum of money is Rs. 165.

---